Problem: Which of these numbers is prime? ${35,\ 45,\ 63,\ 71,\ 72}$
A prime number has exactly two factors: 1 and itself. The factors of 35 are 1, 5, 7, and 35. The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 63 are 1, 3, 7, 9, 21, and 63. The factors of 71 are 1 and 71. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Thus, 71 is a prime number.